Error estimates of the backward Euler-Maruyama method for multi-valued stochastic differential equations
Abstract
In this paper, we derive error estimates of the backward Euler-Maruyama method applied to multi-valued stochastic differential equations. An important example of such an equation is a stochastic gradient flow whose associated potential is not continuously differentiable, but assumed to be convex. We show that the backward Euler-Maruyama method is well-defined and convergent of order at least with respect to the root-mean-square norm. Our error analysis relies on techniques for deterministic problems developed in [Nochetto, Savar\'e, and Verdi, Comm.\ Pure Appl.\ Math., 2000]. We verify that our setting applies to an overdamped Langevin equation with a discontinuous gradient and to a spatially semi-discrete approximation of the stochastic -Laplace equation.
Cite
@article{arxiv.1906.11538,
title = {Error estimates of the backward Euler-Maruyama method for multi-valued stochastic differential equations},
author = {Monika Eisenmann and Mihály Kovács and Raphael Kruse and Stig Larsson},
journal= {arXiv preprint arXiv:1906.11538},
year = {2022}
}